Download Net Force: a resultant force acting on object

Physics 111: Mechanics
Lecture 4
Dale Gary
NJIT Physics Department
The Laws of Motion






Newton’s first law
Force
Mass
Newton’s second law
Newton’s third law
Examples
Isaac Newton’s work represents one of the greatest
contributions to science ever made by an individual.
Feb. 11-15, 2013
Dynamics
Describes the relationship between the motion
of objects in our everyday world and the forces
acting on them
 Language of Dynamics


Force: The measure of interaction between two
objects (pull or push). It is a vector quantity – it has a
magnitude and direction

Mass: The measure of how difficult it is to change
object’s velocity (sluggishness or inertia of the object)
Feb. 11-15, 2013
Forces



The measure of interaction
between two objects (pull or
push)
Vector quantity: has
magnitude and direction
May be a contact force or a
field force


Contact forces result from
physical contact between two
objects
Field forces act between
disconnected objects

Also called “action at a distance”
Feb. 11-15, 2013
Forces

Gravitational Force
 Archimedes Force
 Friction Force
 Tension Force
 Spring Force
 Normal Force
Feb. 11-15, 2013
Vector Nature of Force
Vector force: has magnitude and direction
 Net Force: a resultant force acting on object


   
Fnet   F  F1  F2  F3  ......

You must use the rules of vector addition to
obtain the net force on an object
| F | F12  F22  2.24 N
  tan 1 (
F1
)  26.6
F2
Feb. 11-15, 2013
Newton’s First Law

An object at rest tends to stay at rest and an
object in motion tends to stay in motion with
the same speed and in the same direction
unless acted upon by an unbalanced force

An object at rest remains at rest as long as no net force acts on it
 An object moving with constant velocity continues to move with
the same speed and in the same direction (the same velocity) as
long as no net force acts on it
 “Keep on doing what it is doing”
Feb. 11-15, 2013
Newton’s First Law


When forces are balanced, the acceleration of the object is zero



An object at rest tends to stay at rest and an
object in motion tends to stay in motion with
the same speed and in the same direction
unless acted upon by an unbalanced force
Object at rest: v = 0 and a = 0
Object in motion: v  0 and a = 0
The net force is defined as the vector sum of all the external forces
exerted on the object. If the net force is zero, forces are balanced.
When forces are balances, the object can be stationary, or move
with constant velocity.
Feb. 11-15, 2013
Mass and Inertia

Every object continues in its state of rest, or uniform
motion in a straight line, unless it is compelled to change
that state by unbalanced forces impressed upon it
 Inertia is a property of objects
to resist changes is motion!
 Mass is a measure of the
amount of inertia.
 Mass is a measure of the resistance of an object to
changes in its velocity
 Mass is an inherent property of an object
 Scalar quantity and SI unit: kg
Feb. 11-15, 2013
Newton’s Second Law

The acceleration of an object is directly
proportional to the net force acting on
it and inversely proportional to its mass

F


Fnet
a

m
m



Fnet   F  ma
Feb. 11-15, 2013
Units of Force

Newton’s second law:

SI unit of force is a Newton (N)



Fnet   F  ma
kg m
1 N 1 2
s

US Customary unit of force is a pound (lb)
 1 N = 0.225 lb
 Weight, also measured in lbs. is a force (mass x
acceleration). What is the acceleration in that case?
Feb. 11-15, 2013
More about Newton’s 2nd Law
You must be certain about which body we are
applying it to
 Fnet must be the vector sum of all the forces that act
on that body
 Only forces that act on that body are to be included
in the vector sum
 Net force component along an
axis gives rise to the acceleration
along that same axis

Fnet , x  max
Fnet , y  may
Feb. 11-15, 2013
Sample Problem

One or two forces act on a puck that moves over frictionless ice
along an x axis, in one-dimensional motion. The puck's mass is m =
0.20 kg. Forces F1 and F2 and are directed along the x axis and
have magnitudes F1 = 4.0 N and F2 = 2.0 N. Force F3 is directed at
angle  = 30° and has magnitude F3 = 1.0 N. In each situation, what
is the acceleration of the puck?
a ) F1  max
ax 
F1 4.0 N

 20 m/s 2
m 0.2 kg
b) F1  F2  max
ax 
Fnet , x  max
c) F3, x  F2  max
F1  F2 4.0 N  2.0 N

 10 m/s 2
m
0.2 kg
F3, x  F3 cos 
F3 cos   F2 1.0 N cos 30  2.0 N
ax 

 5.7 m/s 2
m
0.2 kg
Feb. 11-15, 2013
Gravitational Force
Gravitational force is a vector
 Expressed by Newton’s Law of Universal
Gravitation:
mM

Fg  G





R2
G – gravitational constant
M – mass of the Earth
m – mass of an object
R – radius of the Earth
Direction: pointing downward
Feb. 11-15, 2013
Weight



The magnitude of the gravitational force acting on an
object of mass m near the Earth’s surface is called the
weight w of the object: w = mg
g can also be found from the Law of Universal Gravitation
Weight has a unit of N
mM
Fg  G 2
R
w  Fg  mg
M
g  G 2  9.8 m/s 2
R

Weight depends upon location
R = 6,400 km
Feb. 11-15, 2013
Normal Force
Force from a solid
surface which keeps
object from falling
through
 Direction: always
perpendicular to the
surface
 Magnitude: depends
on situation

w  Fg  mg
N  Fg  ma y
N  mg  ma y
N  mg
Feb. 11-15, 2013
Tension Force: T
A taut rope exerts forces
on whatever holds its
ends
 Direction: always along
the cord (rope, cable,
string ……) and away
from the object
T2
 Magnitude: depend on
situation

T1
T1 = T = T2
Feb. 11-15, 2013
Newton’s Third Law

If object 1 and object 2 interact, the force
exerted by object 1 on object 2 is equal in
magnitude but opposite in direction to the
force exerted by object 2 on object 1


Fon A  Fon B

Equivalent to saying a single isolated force cannot exist
Feb. 11-15, 2013
Newton’s Third Law cont.

F12 may be called the
action force and F21 the
reaction force


Actually, either force can
be the action or the
reaction force
The action and reaction
forces act on different
objects
Feb. 11-15, 2013
Some Action-Reaction Pairs
Fg  G
mM
R2
mM
Fg  G 2
R
GM
Fg  mg  m 2
R
Fg  Ma  M
Gm
R2
Feb. 11-15, 2013
Free Body Diagram




The most important step in
solving problems involving
Newton’s Laws is to draw the
free body diagram
Be sure to include only the
forces acting on the object of
interest
Include any field forces acting
on the object
Do not assume the normal
force equals the weight
F hand on book
F Earth on book
Feb. 11-15, 2013
Hints for Problem-Solving







Read the problem carefully at least once
Draw a picture of the system, identify the object of primary interest,
and indicate forces with arrows
Label each force in the picture in a way that will bring to mind what
physical quantity the label stands for (e.g., T for tension)
Draw a free-body diagram of the object of interest, based on the
labeled picture. If additional objects are involved, draw separate
free-body diagram for them
Choose a convenient coordinate system for each object
Apply Newton’s second law. The x- and y-components of Newton
second law should be taken from the vector equation and written
individually. This often results in two equations and two unknowns
Solve for the desired unknown quantity, and substitute the numbers
Fnet , x  max
Fnet , y  may
Feb. 11-15, 2013
Objects in Equilibrium
Objects that are either at rest or moving with
constant velocity are said to be in equilibrium
 Acceleration of an object can be modeled as

zero: a  0
 Mathematically, the net force acting on the

object is zero
F  0
 Equivalent to the set of component equations
given by

F
x
0
F
y
0
Feb. 11-15, 2013
Equilibrium, Example 1
A lamp is suspended from a
chain of negligible mass
 The forces acting on the
lamp are




the downward force of gravity
the upward tension in the
chain
Applying equilibrium gives
F
y
 0  T  Fg  0  T  Fg
Feb. 11-15, 2013
Equilibrium, Example 2

A traffic light weighing 100 N hangs from a vertical cable
tied to two other cables that are fastened to a support.
The upper cables make angles of 37° and 53° with the
horizontal. Find the tension in each of the three cables.

Conceptualize the traffic light



Assume cables don’t break
Nothing is moving
Categorize as an equilibrium problem


No movement, so acceleration is zero
Model as an object in equilibrium
F
x
0
F
y
0
Feb. 11-15, 2013
Equilibrium, Example 2

Need 2 free-body diagrams

Apply equilibrium equation to light
 Fy  0  T3  Fg  0
T3  Fg  100 N

F
y
 0  T3  Fg  0
T3  Fg  100 N
Apply equilibrium equations to knot
F
F
x
 T1x  T2 x  T1 cos 37   T2 cos 53  0
y
 T1 y  T2 y  T3 y
 T1 sin 37   T2 sin 53  100 N  0
 cos 37  
  1.33T1
T2  T1 
 
cos
53


T1  60 N
T2  1.33T1  80 N
Feb. 11-15, 2013
Accelerating Objects
If an object that can be modeled as a particle
experiences an acceleration, there must be a
nonzero net force acting on it
 Draw a free-body diagram
 Apply Newton’s Second Law in component form



 F  ma
F
x
 max
F
y
 may
Feb. 11-15, 2013
Accelerating Objects, Example 1

A man weighs himself with a scale in an elevator. While
the elevator is at rest, he measures a weight of 800 N.



What weight does the scale read if the elevator accelerates
upward at 2.0 m/s2? a = 2.0 m/s2
What weight does the scale read if the elevator accelerates
downward at 2.0 m/s2? a = - 2.0 m/s2
Upward:
F
y
 N  mg  ma
N  mg  ma  m( g  a)
w
800 N
m 
 80 N
g 9.8 m/s 2

N
N  80(2.0  9.8)  624 N
N
N  mg
Downward: N  80(2.0  9.8)  624 N
N  mg
mg
Feb. 11-15, 2013
mg